# Elastic material identifiability experiment workbench

Family 372: Global uniqueness in smooth isotropic elasticity. First source-informed review, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Materials modeling teams can separate ideal uniqueness of smooth isotropic Lamé parameters from practical parameter estimation under sparse displacement and traction measurements.

## Applicability and commercial boundary

The theorem uses the full static displacement-to-traction operator on a bounded connected smooth three-dimensional domain with smooth coefficients, μ>0 and 3λ+2μ>0. The selected formal statement proves uniqueness only and gives no reconstruction algorithm, finite-data stability bound or anisotropic extension.

## Initial business decision

Conditional evidence workflow. Commercial demand and profitability remain hypotheses. Research usefulness is not evidence of a buyer budget.

## Next verification action

Build a measurement coverage and parameter-sensitivity report against an existing finite-element inverse model; measure held-out predictive accuracy independently.

## Evidence scope

The catalog statement and main-paper abstract or introductory theorem passages were individually reviewed. Available family-level scope documents were inspected, with attention to version differences and exclusions. This is a first application triage, not a full proof audit or independent Lean verification. Family 376 has nine paper abstracts inspected; selected scopes are not assumed to cover all nine papers in full. Source revision `fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb`. See [source metadata](source.json).

## Pinned sources

- [Global Uniqueness for the Smooth Isotropic Elasticity Inverse Problem](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Global-Uniqueness-for-the-Smooth-Isotropic-Elasticity-Inverse-Problem-September-24-2026/article.pdf)
- [Selected formal scope](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/lean/docs/372.md)